A multi-model, Bayesian, resampling, sequential experimental design for response surface estimation

Existing response surface techniques do not cope well with multi-model selection. We introduce a multi-model resampling approach as an alternative method in the context of Bayesian sequential experimentation.;The steps required to sequentially identify a response are dictated by the type of model fitted at the previous stage and by the form of the proposed model to be fitted at the current stage. To avoid model inadequacy we simultaneously evaluate not just one model but a set of them.;Our initial approach computes the posterior odds associated with linear functions with normal errors. This approach is extended to non-normal and non-homogeneous errors by introducing a general resampling algorithm (GRA). The GRA overcomes the need to assume normality and allows model bias to be dealt with independent of the estimation process.;The GRA was also designed to simultaneously select between multiple response models and to estimate their parameters. It also provides the capacity to evaluate the best experimental locations for estimating the model parameters. Even under non-homogeneous errors the GRA provides a robust method for the selection of a response model.;The GRA works like an "oracle" by providing an easy method to evaluate the location of potential next observations. Its power lies not only in the selection of a model to estimate the response, but in doing so with less experimentation than that associated with existing techniques.